War - however long it will take
They also agreed on a role for the United Nations in a postwar Iraq.
"We have one objective in mind victory," Mr Bush said.
Mr Blair said the coalition's agenda is "not set by time, it's set by the nature of the job".
Mr Bush and Mr Blair, in a joint news conference at Camp David, called for an immediate resumption of the UN "Oil for Food" programme to help speed the distribution of food and medical supplies to Iraqis. The programme allows Iraqis to sell unlimited quantities of oil as long as the money goes mainly to buy food, medicine and other humanitarian goods for Iraq's people. About 60% of Iraq's 22 million people are fed through the programme, which was suspended with the onset of war.
Both leaders gave an upbeat assessment of what had been accomplished during the first week of the war.
"Together, coalition forces are advancing day by day in steady progress against the enemy," Mr Bush said.
Even so, neither Mr Bush nor Mr Blair would set a timetable for the war's conclusion.
"However long it takes to win. However long it takes to achieve our objective. However long it takes," Mr Bush said. "It's not a matter of timetable, it's a matter of victory."
Mr Bush and Mr Blair were briefed on the progress of the war in Iraq after a week of fierce combat, and their meeting took place amid growing signs that Iraqi forces have dug in for a prolonged fight.
Mr Blair said he and Mr Bush had decided to seek new UN resolutions on humanitarian relief, a postwar administration for Iraq and a promise to keep Iraq's territorial boundaries intact.
But differences appeared to remain on the extent of the UN role in governing. Mr Blair has advocated a more aggressive role for the world body in a post-war government than Mr Bush.
"No doubt, the United Nations has got to be closely involved in this process," Mr Blair said. He said he and Mr Bush agreed on "principles" but there are "huge numbers of details to be discussed with our allies as to exactly how that is going to work".
Mr Blair and Mr Bush appeared in front of a display of British and American flags in a helicopter hangar on the grounds of the secluded presidential retreat. "Iraq will be disarmed of weapons of mass destruction. And the Iraqi people will be freed. That is our commitment. That is our determination, and we will see it done," Mr Blair said.
In Washington, at a Senate hearing yesterday, Defence Secretary Donald Rumsfeld was asked about diplomatic efforts by Arab nations or the UN to arrange a ceasefire.
"I have no idea what some country might propose, but there isn't going to be a ceasefire," Mr Rumsfeld told a Senate Appropriations panel.
Mr Bush said anew that any Iraqi that launched chemical or biological weapons against US-led forces "will be tried as a war criminal".
Mr Blair referred to the deaths of two British soldiers, saying they had been executed.
"It is an act of cruelty beyond all human comprehension," he said.
Both Mr Bush and Mr Blair addressed the lack of support among many traditional allies in war. "There are many people on our side, there are those that oppose us," Mr Blair acknowledged. But he also said he had "no doubt that our cause is just."
Mr Bush insisted: "We have plenty of Western allies. We can give you a list."
Mr Blair said the US and its allies must broaden their agenda beyond Iraq to help build peace in the Middle East and across the globe.
Mr Bush arrived at his retreat in Maryland's Catoctin Mountains on Wednesday afternoon following a quick trip to Florida, where he'd sought to rally the troops and the American people behind the Iraq war at a time when US forces are suffering casualties.
